First of all you need to get the mortgage approval for the whole of the mortgage, with out that you cant go anywhere. I would re-finance with your current lender, they can see your payment history if they refuse then try else where. You dont state you current income or any other out goings and not to be negative but a post on here a few weeks ago......married couple joint income of 95k no other outstanding debts were refused a mortgage of 250k ( i think it was 200 and something anyway ) they wern't just refused by one lender either.
I think your brother is losing out.... why is he selling now? House prices are way down....good for you bad for him....anyway.
In figuring out how much you would need to buy your brother out is going to be tricky, are you going to take into account the money you put into furnishing the house any repairs ect the money that he has paid towards the mortgage so far? It's not just about what value is left in the house after you take away the outstanding mortgage. Are you going to split the legal fees ect. Did you both put half into the deposit?
The simple way is to imagine you are selling the house, you sell the house for 300k and there's 200k outstanding on the mortgage. Say 10k for legal fees and anything else so you're left with 90k. You would both get 45k So to buy him out you would need to give him 45k. Now thats a very simple way but it wont just come down to that.